Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- (x-3)√x^2-√1<0
- (x^2-7|x|+10)/(x^2-6x+9)>=0
- 5x^2-2x^4+7>0
- 1−4x<2x+23−x−12
- Derivative of:
-
cos(t)
- Limit of the function:
-
cos(t)
-
1/5
- Integral of d{x}:
- cos(t)
-
1/5
- Sum of series:
-
1/5
-
Identical expressions
- cos(t)< one / five
- co sinus of e of (t) less than 1 divide by 5
- co sinus of e of (t) less than one divide by five
- cost<1/5
- cos(t)<1 divide by 5
-
Similar expressions
- cost>=-sqrt(2)/2
cos(t)<1/5 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} < \frac{1}{5}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{5}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{5}$$
transform
$$\cos{\left(t \right)} - \frac{1}{5} = 0$$
$$\cos{\left(t \right)} - \frac{1}{5} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{5}$$
We get the answer: w = 1/5
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 32.7853649419025$$
$$x_{2} = -11.1969322083546$$
$$x_{3} = 7.65262371318415$$
$$x_{4} = -13.9358090203637$$
$$x_{5} = -95.6172180136984$$
$$x_{6} = 92.8783412016892$$
$$x_{7} = -57.9181061706208$$
$$x_{8} = 45.3517355562617$$
$$x_{9} = -89.3340327065188$$
$$x_{10} = 57.9181061706208$$
$$x_{11} = 83.0508473993392$$
$$x_{12} = 39.0685502490821$$
$$x_{13} = -32.7853649419025$$
$$x_{14} = 13.9358090203637$$
$$x_{15} = -86.5951558945096$$
$$x_{16} = 80.3119705873301$$
$$x_{17} = 1.36943840600457$$
$$x_{18} = 64.2012914778004$$
$$x_{19} = 61.4624146657913$$
$$x_{20} = -17.4801175155342$$
$$x_{21} = -83.0508473993392$$
$$x_{22} = 55.1792293586117$$
$$x_{23} = 89.3340327065188$$
$$x_{24} = 48.8960440514321$$
$$x_{25} = 23.7633028227138$$
$$x_{26} = -36.329673437073$$
$$x_{27} = 17.4801175155342$$
$$x_{28} = -48.8960440514321$$
$$x_{29} = -4.91374690117502$$
$$x_{30} = 76.7676620921596$$
$$x_{31} = -99.1615265088688$$
$$x_{32} = -45.3517355562617$$
$$x_{33} = 36.329673437073$$
$$x_{34} = -23.7633028227138$$
$$x_{35} = 95.6172180136984$$
$$x_{36} = 99.1615265088688$$
$$x_{37} = -55.1792293586117$$
$$x_{38} = 67.7455999729709$$
$$x_{39} = 20.2189943275433$$
$$x_{40} = -26.5021796347229$$
$$x_{41} = -64.2012914778004$$
$$x_{42} = -80.3119705873301$$
$$x_{43} = 74.0287852801505$$
$$x_{44} = 86.5951558945096$$
$$x_{45} = 4.91374690117502$$
$$x_{46} = -70.48447678498$$
$$x_{47} = -51.6349208634413$$
$$x_{48} = 30.0464881298934$$
$$x_{49} = -30.0464881298934$$
$$x_{50} = -76.7676620921596$$
$$x_{51} = 70.48447678498$$
$$x_{52} = -92.8783412016892$$
$$x_{53} = -39.0685502490821$$
$$x_{54} = 834.29420744888$$
$$x_{55} = -654.820710352682$$
$$x_{56} = 11.1969322083546$$
$$x_{57} = -42.6128587442525$$
$$x_{58} = -20.2189943275433$$
$$x_{59} = 51.6349208634413$$
$$x_{60} = 108.183588628058$$
$$x_{61} = -67.7455999729709$$
$$x_{62} = -61.4624146657913$$
$$x_{63} = 42.6128587442525$$
$$x_{64} = -7.65262371318415$$
$$x_{65} = -1.36943840600457$$
$$x_{66} = -74.0287852801505$$
$$x_{67} = 26.5021796347229$$
$$x_{1} = 32.7853649419025$$
$$x_{2} = -11.1969322083546$$
$$x_{3} = 7.65262371318415$$
$$x_{4} = -13.9358090203637$$
$$x_{5} = -95.6172180136984$$
$$x_{6} = 92.8783412016892$$
$$x_{7} = -57.9181061706208$$
$$x_{8} = 45.3517355562617$$
$$x_{9} = -89.3340327065188$$
$$x_{10} = 57.9181061706208$$
$$x_{11} = 83.0508473993392$$
$$x_{12} = 39.0685502490821$$
$$x_{13} = -32.7853649419025$$
$$x_{14} = 13.9358090203637$$
$$x_{15} = -86.5951558945096$$
$$x_{16} = 80.3119705873301$$
$$x_{17} = 1.36943840600457$$
$$x_{18} = 64.2012914778004$$
$$x_{19} = 61.4624146657913$$
$$x_{20} = -17.4801175155342$$
$$x_{21} = -83.0508473993392$$
$$x_{22} = 55.1792293586117$$
$$x_{23} = 89.3340327065188$$
$$x_{24} = 48.8960440514321$$
$$x_{25} = 23.7633028227138$$
$$x_{26} = -36.329673437073$$
$$x_{27} = 17.4801175155342$$
$$x_{28} = -48.8960440514321$$
$$x_{29} = -4.91374690117502$$
$$x_{30} = 76.7676620921596$$
$$x_{31} = -99.1615265088688$$
$$x_{32} = -45.3517355562617$$
$$x_{33} = 36.329673437073$$
$$x_{34} = -23.7633028227138$$
$$x_{35} = 95.6172180136984$$
$$x_{36} = 99.1615265088688$$
$$x_{37} = -55.1792293586117$$
$$x_{38} = 67.7455999729709$$
$$x_{39} = 20.2189943275433$$
$$x_{40} = -26.5021796347229$$
$$x_{41} = -64.2012914778004$$
$$x_{42} = -80.3119705873301$$
$$x_{43} = 74.0287852801505$$
$$x_{44} = 86.5951558945096$$
$$x_{45} = 4.91374690117502$$
$$x_{46} = -70.48447678498$$
$$x_{47} = -51.6349208634413$$
$$x_{48} = 30.0464881298934$$
$$x_{49} = -30.0464881298934$$
$$x_{50} = -76.7676620921596$$
$$x_{51} = 70.48447678498$$
$$x_{52} = -92.8783412016892$$
$$x_{53} = -39.0685502490821$$
$$x_{54} = 834.29420744888$$
$$x_{55} = -654.820710352682$$
$$x_{56} = 11.1969322083546$$
$$x_{57} = -42.6128587442525$$
$$x_{58} = -20.2189943275433$$
$$x_{59} = 51.6349208634413$$
$$x_{60} = 108.183588628058$$
$$x_{61} = -67.7455999729709$$
$$x_{62} = -61.4624146657913$$
$$x_{63} = 42.6128587442525$$
$$x_{64} = -7.65262371318415$$
$$x_{65} = -1.36943840600457$$
$$x_{66} = -74.0287852801505$$
$$x_{67} = 26.5021796347229$$
This roots
$$x_{55} = -654.820710352682$$
$$x_{31} = -99.1615265088688$$
$$x_{5} = -95.6172180136984$$
$$x_{52} = -92.8783412016892$$
$$x_{9} = -89.3340327065188$$
$$x_{15} = -86.5951558945096$$
$$x_{21} = -83.0508473993392$$
$$x_{42} = -80.3119705873301$$
$$x_{50} = -76.7676620921596$$
$$x_{66} = -74.0287852801505$$
$$x_{46} = -70.48447678498$$
$$x_{61} = -67.7455999729709$$
$$x_{41} = -64.2012914778004$$
$$x_{62} = -61.4624146657913$$
$$x_{7} = -57.9181061706208$$
$$x_{37} = -55.1792293586117$$
$$x_{47} = -51.6349208634413$$
$$x_{28} = -48.8960440514321$$
$$x_{32} = -45.3517355562617$$
$$x_{57} = -42.6128587442525$$
$$x_{53} = -39.0685502490821$$
$$x_{26} = -36.329673437073$$
$$x_{13} = -32.7853649419025$$
$$x_{49} = -30.0464881298934$$
$$x_{40} = -26.5021796347229$$
$$x_{34} = -23.7633028227138$$
$$x_{58} = -20.2189943275433$$
$$x_{20} = -17.4801175155342$$
$$x_{4} = -13.9358090203637$$
$$x_{2} = -11.1969322083546$$
$$x_{64} = -7.65262371318415$$
$$x_{29} = -4.91374690117502$$
$$x_{65} = -1.36943840600457$$
$$x_{17} = 1.36943840600457$$
$$x_{45} = 4.91374690117502$$
$$x_{3} = 7.65262371318415$$
$$x_{56} = 11.1969322083546$$
$$x_{14} = 13.9358090203637$$
$$x_{27} = 17.4801175155342$$
$$x_{39} = 20.2189943275433$$
$$x_{25} = 23.7633028227138$$
$$x_{67} = 26.5021796347229$$
$$x_{48} = 30.0464881298934$$
$$x_{1} = 32.7853649419025$$
$$x_{33} = 36.329673437073$$
$$x_{12} = 39.0685502490821$$
$$x_{63} = 42.6128587442525$$
$$x_{8} = 45.3517355562617$$
$$x_{24} = 48.8960440514321$$
$$x_{59} = 51.6349208634413$$
$$x_{22} = 55.1792293586117$$
$$x_{10} = 57.9181061706208$$
$$x_{19} = 61.4624146657913$$
$$x_{18} = 64.2012914778004$$
$$x_{38} = 67.7455999729709$$
$$x_{51} = 70.48447678498$$
$$x_{43} = 74.0287852801505$$
$$x_{30} = 76.7676620921596$$
$$x_{16} = 80.3119705873301$$
$$x_{11} = 83.0508473993392$$
$$x_{44} = 86.5951558945096$$
$$x_{23} = 89.3340327065188$$
$$x_{6} = 92.8783412016892$$
$$x_{35} = 95.6172180136984$$
$$x_{36} = 99.1615265088688$$
$$x_{60} = 108.183588628058$$
$$x_{54} = 834.29420744888$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{55}$$
For example, let's take the point
$$x_{0} = x_{55} - \frac{1}{10}$$
=
$$-654.820710352682 + - \frac{1}{10}$$
=
$$-654.920710352682$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{5}$$
$$\cos{\left(t \right)} < \frac{1}{5}$$
Then
$$x < -654.820710352682$$
no execute
one of the solutions of our inequality is:
$$x > -654.820710352682 \wedge x < -99.1615265088688$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -654.820710352682 \wedge x < -99.1615265088688$$
$$x > -95.6172180136984 \wedge x < -92.8783412016892$$
$$x > -89.3340327065188 \wedge x < -86.5951558945096$$
$$x > -83.0508473993392 \wedge x < -80.3119705873301$$
$$x > -76.7676620921596 \wedge x < -74.0287852801505$$
$$x > -70.48447678498 \wedge x < -67.7455999729709$$
$$x > -64.2012914778004 \wedge x < -61.4624146657913$$
$$x > -57.9181061706208 \wedge x < -55.1792293586117$$
$$x > -51.6349208634413 \wedge x < -48.8960440514321$$
$$x > -45.3517355562617 \wedge x < -42.6128587442525$$
$$x > -39.0685502490821 \wedge x < -36.329673437073$$
$$x > -32.7853649419025 \wedge x < -30.0464881298934$$
$$x > -26.5021796347229 \wedge x < -23.7633028227138$$
$$x > -20.2189943275433 \wedge x < -17.4801175155342$$
$$x > -13.9358090203637 \wedge x < -11.1969322083546$$
$$x > -7.65262371318415 \wedge x < -4.91374690117502$$
$$x > -1.36943840600457 \wedge x < 1.36943840600457$$
$$x > 4.91374690117502 \wedge x < 7.65262371318415$$
$$x > 11.1969322083546 \wedge x < 13.9358090203637$$
$$x > 17.4801175155342 \wedge x < 20.2189943275433$$
$$x > 23.7633028227138 \wedge x < 26.5021796347229$$
$$x > 30.0464881298934 \wedge x < 32.7853649419025$$
$$x > 36.329673437073 \wedge x < 39.0685502490821$$
$$x > 42.6128587442525 \wedge x < 45.3517355562617$$
$$x > 48.8960440514321 \wedge x < 51.6349208634413$$
$$x > 55.1792293586117 \wedge x < 57.9181061706208$$
$$x > 61.4624146657913 \wedge x < 64.2012914778004$$
$$x > 67.7455999729709 \wedge x < 70.48447678498$$
$$x > 74.0287852801505 \wedge x < 76.7676620921596$$
$$x > 80.3119705873301 \wedge x < 83.0508473993392$$
$$x > 86.5951558945096 \wedge x < 89.3340327065188$$
$$x > 92.8783412016892 \wedge x < 95.6172180136984$$
$$x > 99.1615265088688 \wedge x < 108.183588628058$$
$$x > 834.29420744888$$
$$\cos{\left(t \right)} < \frac{1}{5}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{5}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{5}$$
transform
$$\cos{\left(t \right)} - \frac{1}{5} = 0$$
$$\cos{\left(t \right)} - \frac{1}{5} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{5}$$
We get the answer: w = 1/5
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 32.7853649419025$$
$$x_{2} = -11.1969322083546$$
$$x_{3} = 7.65262371318415$$
$$x_{4} = -13.9358090203637$$
$$x_{5} = -95.6172180136984$$
$$x_{6} = 92.8783412016892$$
$$x_{7} = -57.9181061706208$$
$$x_{8} = 45.3517355562617$$
$$x_{9} = -89.3340327065188$$
$$x_{10} = 57.9181061706208$$
$$x_{11} = 83.0508473993392$$
$$x_{12} = 39.0685502490821$$
$$x_{13} = -32.7853649419025$$
$$x_{14} = 13.9358090203637$$
$$x_{15} = -86.5951558945096$$
$$x_{16} = 80.3119705873301$$
$$x_{17} = 1.36943840600457$$
$$x_{18} = 64.2012914778004$$
$$x_{19} = 61.4624146657913$$
$$x_{20} = -17.4801175155342$$
$$x_{21} = -83.0508473993392$$
$$x_{22} = 55.1792293586117$$
$$x_{23} = 89.3340327065188$$
$$x_{24} = 48.8960440514321$$
$$x_{25} = 23.7633028227138$$
$$x_{26} = -36.329673437073$$
$$x_{27} = 17.4801175155342$$
$$x_{28} = -48.8960440514321$$
$$x_{29} = -4.91374690117502$$
$$x_{30} = 76.7676620921596$$
$$x_{31} = -99.1615265088688$$
$$x_{32} = -45.3517355562617$$
$$x_{33} = 36.329673437073$$
$$x_{34} = -23.7633028227138$$
$$x_{35} = 95.6172180136984$$
$$x_{36} = 99.1615265088688$$
$$x_{37} = -55.1792293586117$$
$$x_{38} = 67.7455999729709$$
$$x_{39} = 20.2189943275433$$
$$x_{40} = -26.5021796347229$$
$$x_{41} = -64.2012914778004$$
$$x_{42} = -80.3119705873301$$
$$x_{43} = 74.0287852801505$$
$$x_{44} = 86.5951558945096$$
$$x_{45} = 4.91374690117502$$
$$x_{46} = -70.48447678498$$
$$x_{47} = -51.6349208634413$$
$$x_{48} = 30.0464881298934$$
$$x_{49} = -30.0464881298934$$
$$x_{50} = -76.7676620921596$$
$$x_{51} = 70.48447678498$$
$$x_{52} = -92.8783412016892$$
$$x_{53} = -39.0685502490821$$
$$x_{54} = 834.29420744888$$
$$x_{55} = -654.820710352682$$
$$x_{56} = 11.1969322083546$$
$$x_{57} = -42.6128587442525$$
$$x_{58} = -20.2189943275433$$
$$x_{59} = 51.6349208634413$$
$$x_{60} = 108.183588628058$$
$$x_{61} = -67.7455999729709$$
$$x_{62} = -61.4624146657913$$
$$x_{63} = 42.6128587442525$$
$$x_{64} = -7.65262371318415$$
$$x_{65} = -1.36943840600457$$
$$x_{66} = -74.0287852801505$$
$$x_{67} = 26.5021796347229$$
$$x_{1} = 32.7853649419025$$
$$x_{2} = -11.1969322083546$$
$$x_{3} = 7.65262371318415$$
$$x_{4} = -13.9358090203637$$
$$x_{5} = -95.6172180136984$$
$$x_{6} = 92.8783412016892$$
$$x_{7} = -57.9181061706208$$
$$x_{8} = 45.3517355562617$$
$$x_{9} = -89.3340327065188$$
$$x_{10} = 57.9181061706208$$
$$x_{11} = 83.0508473993392$$
$$x_{12} = 39.0685502490821$$
$$x_{13} = -32.7853649419025$$
$$x_{14} = 13.9358090203637$$
$$x_{15} = -86.5951558945096$$
$$x_{16} = 80.3119705873301$$
$$x_{17} = 1.36943840600457$$
$$x_{18} = 64.2012914778004$$
$$x_{19} = 61.4624146657913$$
$$x_{20} = -17.4801175155342$$
$$x_{21} = -83.0508473993392$$
$$x_{22} = 55.1792293586117$$
$$x_{23} = 89.3340327065188$$
$$x_{24} = 48.8960440514321$$
$$x_{25} = 23.7633028227138$$
$$x_{26} = -36.329673437073$$
$$x_{27} = 17.4801175155342$$
$$x_{28} = -48.8960440514321$$
$$x_{29} = -4.91374690117502$$
$$x_{30} = 76.7676620921596$$
$$x_{31} = -99.1615265088688$$
$$x_{32} = -45.3517355562617$$
$$x_{33} = 36.329673437073$$
$$x_{34} = -23.7633028227138$$
$$x_{35} = 95.6172180136984$$
$$x_{36} = 99.1615265088688$$
$$x_{37} = -55.1792293586117$$
$$x_{38} = 67.7455999729709$$
$$x_{39} = 20.2189943275433$$
$$x_{40} = -26.5021796347229$$
$$x_{41} = -64.2012914778004$$
$$x_{42} = -80.3119705873301$$
$$x_{43} = 74.0287852801505$$
$$x_{44} = 86.5951558945096$$
$$x_{45} = 4.91374690117502$$
$$x_{46} = -70.48447678498$$
$$x_{47} = -51.6349208634413$$
$$x_{48} = 30.0464881298934$$
$$x_{49} = -30.0464881298934$$
$$x_{50} = -76.7676620921596$$
$$x_{51} = 70.48447678498$$
$$x_{52} = -92.8783412016892$$
$$x_{53} = -39.0685502490821$$
$$x_{54} = 834.29420744888$$
$$x_{55} = -654.820710352682$$
$$x_{56} = 11.1969322083546$$
$$x_{57} = -42.6128587442525$$
$$x_{58} = -20.2189943275433$$
$$x_{59} = 51.6349208634413$$
$$x_{60} = 108.183588628058$$
$$x_{61} = -67.7455999729709$$
$$x_{62} = -61.4624146657913$$
$$x_{63} = 42.6128587442525$$
$$x_{64} = -7.65262371318415$$
$$x_{65} = -1.36943840600457$$
$$x_{66} = -74.0287852801505$$
$$x_{67} = 26.5021796347229$$
This roots
$$x_{55} = -654.820710352682$$
$$x_{31} = -99.1615265088688$$
$$x_{5} = -95.6172180136984$$
$$x_{52} = -92.8783412016892$$
$$x_{9} = -89.3340327065188$$
$$x_{15} = -86.5951558945096$$
$$x_{21} = -83.0508473993392$$
$$x_{42} = -80.3119705873301$$
$$x_{50} = -76.7676620921596$$
$$x_{66} = -74.0287852801505$$
$$x_{46} = -70.48447678498$$
$$x_{61} = -67.7455999729709$$
$$x_{41} = -64.2012914778004$$
$$x_{62} = -61.4624146657913$$
$$x_{7} = -57.9181061706208$$
$$x_{37} = -55.1792293586117$$
$$x_{47} = -51.6349208634413$$
$$x_{28} = -48.8960440514321$$
$$x_{32} = -45.3517355562617$$
$$x_{57} = -42.6128587442525$$
$$x_{53} = -39.0685502490821$$
$$x_{26} = -36.329673437073$$
$$x_{13} = -32.7853649419025$$
$$x_{49} = -30.0464881298934$$
$$x_{40} = -26.5021796347229$$
$$x_{34} = -23.7633028227138$$
$$x_{58} = -20.2189943275433$$
$$x_{20} = -17.4801175155342$$
$$x_{4} = -13.9358090203637$$
$$x_{2} = -11.1969322083546$$
$$x_{64} = -7.65262371318415$$
$$x_{29} = -4.91374690117502$$
$$x_{65} = -1.36943840600457$$
$$x_{17} = 1.36943840600457$$
$$x_{45} = 4.91374690117502$$
$$x_{3} = 7.65262371318415$$
$$x_{56} = 11.1969322083546$$
$$x_{14} = 13.9358090203637$$
$$x_{27} = 17.4801175155342$$
$$x_{39} = 20.2189943275433$$
$$x_{25} = 23.7633028227138$$
$$x_{67} = 26.5021796347229$$
$$x_{48} = 30.0464881298934$$
$$x_{1} = 32.7853649419025$$
$$x_{33} = 36.329673437073$$
$$x_{12} = 39.0685502490821$$
$$x_{63} = 42.6128587442525$$
$$x_{8} = 45.3517355562617$$
$$x_{24} = 48.8960440514321$$
$$x_{59} = 51.6349208634413$$
$$x_{22} = 55.1792293586117$$
$$x_{10} = 57.9181061706208$$
$$x_{19} = 61.4624146657913$$
$$x_{18} = 64.2012914778004$$
$$x_{38} = 67.7455999729709$$
$$x_{51} = 70.48447678498$$
$$x_{43} = 74.0287852801505$$
$$x_{30} = 76.7676620921596$$
$$x_{16} = 80.3119705873301$$
$$x_{11} = 83.0508473993392$$
$$x_{44} = 86.5951558945096$$
$$x_{23} = 89.3340327065188$$
$$x_{6} = 92.8783412016892$$
$$x_{35} = 95.6172180136984$$
$$x_{36} = 99.1615265088688$$
$$x_{60} = 108.183588628058$$
$$x_{54} = 834.29420744888$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{55}$$
For example, let's take the point
$$x_{0} = x_{55} - \frac{1}{10}$$
=
$$-654.820710352682 + - \frac{1}{10}$$
=
$$-654.920710352682$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{5}$$
$$\cos{\left(t \right)} < \frac{1}{5}$$
cos(t) < 1/5
Then
$$x < -654.820710352682$$
no execute
one of the solutions of our inequality is:
$$x > -654.820710352682 \wedge x < -99.1615265088688$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x55 x31 x5 x52 x9 x15 x21 x42 x50 x66 x46 x61 x41 x62 x7 x37 x47 x28 x32 x57 x53 x26 x13 x49 x40 x34 x58 x20 x4 x2 x64 x29 x65 x17 x45 x3 x56 x14 x27 x39 x25 x67 x48 x1 x33 x12 x63 x8 x24 x59 x22 x10 x19 x18 x38 x51 x43 x30 x16 x11 x44 x23 x6 x35 x36 x60 x54Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -654.820710352682 \wedge x < -99.1615265088688$$
$$x > -95.6172180136984 \wedge x < -92.8783412016892$$
$$x > -89.3340327065188 \wedge x < -86.5951558945096$$
$$x > -83.0508473993392 \wedge x < -80.3119705873301$$
$$x > -76.7676620921596 \wedge x < -74.0287852801505$$
$$x > -70.48447678498 \wedge x < -67.7455999729709$$
$$x > -64.2012914778004 \wedge x < -61.4624146657913$$
$$x > -57.9181061706208 \wedge x < -55.1792293586117$$
$$x > -51.6349208634413 \wedge x < -48.8960440514321$$
$$x > -45.3517355562617 \wedge x < -42.6128587442525$$
$$x > -39.0685502490821 \wedge x < -36.329673437073$$
$$x > -32.7853649419025 \wedge x < -30.0464881298934$$
$$x > -26.5021796347229 \wedge x < -23.7633028227138$$
$$x > -20.2189943275433 \wedge x < -17.4801175155342$$
$$x > -13.9358090203637 \wedge x < -11.1969322083546$$
$$x > -7.65262371318415 \wedge x < -4.91374690117502$$
$$x > -1.36943840600457 \wedge x < 1.36943840600457$$
$$x > 4.91374690117502 \wedge x < 7.65262371318415$$
$$x > 11.1969322083546 \wedge x < 13.9358090203637$$
$$x > 17.4801175155342 \wedge x < 20.2189943275433$$
$$x > 23.7633028227138 \wedge x < 26.5021796347229$$
$$x > 30.0464881298934 \wedge x < 32.7853649419025$$
$$x > 36.329673437073 \wedge x < 39.0685502490821$$
$$x > 42.6128587442525 \wedge x < 45.3517355562617$$
$$x > 48.8960440514321 \wedge x < 51.6349208634413$$
$$x > 55.1792293586117 \wedge x < 57.9181061706208$$
$$x > 61.4624146657913 \wedge x < 64.2012914778004$$
$$x > 67.7455999729709 \wedge x < 70.48447678498$$
$$x > 74.0287852801505 \wedge x < 76.7676620921596$$
$$x > 80.3119705873301 \wedge x < 83.0508473993392$$
$$x > 86.5951558945096 \wedge x < 89.3340327065188$$
$$x > 92.8783412016892 \wedge x < 95.6172180136984$$
$$x > 99.1615265088688 \wedge x < 108.183588628058$$
$$x > 834.29420744888$$
Rapid solution
[src]
/ / ___\ / ___\ \ And\t < - atan\2*\/ 6 / + 2*pi, atan\2*\/ 6 / < t/
$$t < - \operatorname{atan}{\left(2 \sqrt{6} \right)} + 2 \pi \wedge \operatorname{atan}{\left(2 \sqrt{6} \right)} < t$$
(atan(2*sqrt(6)) < t)∧(t < -atan(2*sqrt(6)) + 2*pi)
Rapid solution 2
[src]
/ ___\ / ___\ (atan\2*\/ 6 /, - atan\2*\/ 6 / + 2*pi)
$$x\ in\ \left(\operatorname{atan}{\left(2 \sqrt{6} \right)}, - \operatorname{atan}{\left(2 \sqrt{6} \right)} + 2 \pi\right)$$
x in Interval.open(atan(2*sqrt(6)), -atan(2*sqrt(6)) + 2*pi)